First, I'm not a Miele tech. I recommend contacting your vendor or the MFR for support. Check your warranty.
*** the following is for information only ***
* I've worked on table top "Super Automatic" brewers and not a fan of these small units. Similar to the larger Supers, these are the home/office style units. But all have the same problems as the larger professional units. They all require daily maintenance to be performed in order to maintain it. The reason is that these Super Automatics try to replace a Barista. It takes time, training, and lots of practice to become a good Barista. But now with a touch of a button, this 'Robotic machine' will make your favorite Latte for you. But you must keep this robot clean and serviced in order to keep producing coffee (especially milk products like Latte's)
* If you haven't opened up the machine, here is a link;https://www.bing.com/videos/search?q=for+miele+cva+4075&&view=detail&mid=B3EFF641EE5260CB49EBB3EFF641EE5260CB49EB&&FORM=VRDGAR* following this link will also get related vids that may take you to the section your looking for. Be aware that the most likely cause of a problem is coffee grounds, water spills, and old milk getting in the wrong place and needs to be removed to function correctly.
* There are 2 basic systems in the machine for the water portion: Main heater for coffee brewing and steamer heater for the steam wand.
* Whole bean system has; Hopper, Grinder, Volume doser and/or timer.
* Group system compresses the coffee, doses a volume of hot water, then disposes the dregs or 'puck' This is usually a mechanical system with motor and gears.
* There may be an additional steam heater system if there is a Coco/hot chocolate option.
* All Heater systems have a pump (usually vibration), Heater, Thermostat(disk), Thermo fuse.
* Super Automatics always have a digital component to them. Many have options that require not only the correct PC board but also the correct PROM installed (internal programing). Most MFR's will only provide the block diagram of a unit with only a layout of where the cables attach to the PC board.
* Table units have many more sensors than their larger brothers which only check on water temps and how many pucks in the dregs drawer. Table units check the bean level, ground coffee, water level, water temps, group compression(by position), dregs level, panel doors, drip tray present, milk temp(an option), and others that may be on the CPU board as a time out or current usage. Some sensors are physical like a temp probe or a simple micro switch which are easy to find and locate by following the wires. The PC board is another mater. I suspect the MFR has a plug in unit that tests all the functions. I've used another 'good working' unit to swap test the PC boards and plug in parts. But found that PC boards have PROMs that differ from date of MFR and version. So a board may work in one version but not in another.
* Check out the you tube vids as many have come across the common problems. You will note that most are related to cleaning (or the absence) the machine. The other problem is "Opps" and walking away. People will pour stuff into the machine thinking "I thought that's where the milk goes?" or "I wanted a coco, not coffee."
* Air bubbles in the water line(s) from not re-filling the water tank. May require removing the water hose to the pump or detaching the pump from the heater to allow water to flush out the air. Restarting the machine several times may push out the air.
* Final, call vendor for help and service (if available). When I worked on these machines., these units had been swapped out by the seller whom replaced them with newer units to satisfy the customer (Hotel). The seller asked an espresso service company (us) to take a look at them figuring it's cheaper than sending them back to the mainland USA (I'm in Hawaii). So your getting the idea how hard it is to service these units.
* Once operational. Follow the daily maintenance. (and keep a look out for "Opps" people.
Aloha, ukeboy57

First, I'm not a Miele technician, but I've worked on similar table top espresso machines. But I suggest you contact your vendor for service. Check your warranty.
*** Following is just for information***
FYI; There are quite a few you tube videos on this machine.
* These smaller units have individual heaters and mini-boilers instead of one big boiler used in commercial machines.
* I suspect the steamer is a mini-boiler that are common on small brewers. It's about 3" x 4" and 1" thick made of aluminum. There is a heat limit fuse and thermo disk. One or both may be blown.
* If your getting sputtering cold water from the steam wand then it's definitely the boiler other wise it's the vibration pump. Quite a few vids on you tube about the ULKA water pump (suggest alexis c vid)
* I don't think there is any solenoid steam valve on this unit as it's only used on larger boiler systems where the boiler is under pressure all the time. The slow steam start is a good indication of the mini-boiler reheating.
* Final; This is a very compact machine with a lot of wires. Please review the vids on you tube by searching "Miele CVA 4070" Suggest getting help from your vendor as you will need those parts as mentioned.
Aloha, ukeboy57

PS there is a lock out feature on this brand. Check this link for more info:
https://www.bing.com/videos/search?q=Miele+4070&&view=detail&mid=87B4106BEC0DAF1D524587B4106BEC0DAF1D5245&rvsmid=9D76B03F2F848C9C94B59D76B03F2F848C9C94B5&FORM=VDQVAP

I had this problem ... you need to remove the dispenser from the rear of the door. Then once removed clean in running water. Its a sealed unit but you can squirt high pressure water inside to dislodge the coffee sludge. When clean .. fill with water and make sure the 2 spouts drain evenly. regards

Sounds as if the grinder and or the coffee chute is plugged with grounds, this can happen when using a very fine grind and /or a very oily bean. Sometimes the grinder can be cleared when taken all apart and cleaned with a tooth brush - but this would require a service tech for the most part - have to take quite a bit apart to do this

If the Hot water and the steam function work fine - then I would say the water system and heaters are good. Are the grounds being dumped in the waste dry? I would guess so. The brew unit drive sounds to be the issue - it has a valve on it that dumps the water to waste if the pressure is to great - the waste valve sometimes gets stuck, but in your scenario it sounds as if the brew unit is not being driven to full compression (the clicking sound) and if that is the case the operation is cancelled. One thing you may try - set the grind to coarse and try a small cup - this is easier on the drive and may work - showing the Valve is good and the brew unit drive is starting to weaken.
Hope that helps

That looks very similar but not quite the same shapes as Krups have on their XP9000 model. In case you don't know what it's for it wipes without touching across the tamping piston grille to clear any old grounds off that may have stuck on. If you understand the purpose it may help to figure out the where and how. Machine will make a few coffees without it if you need a caffeine fix. On the Krups it would clip around that winged bit of plastic by your thumbnail in the photo. Looks tro me like the brew units are made in the same place with subtle differences for brand & model.